Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Interpret and analyze information in various formats.
• Apply appropriate mathematical calculations to solve problems.
• Integrate different mathematical concepts to find solutions.
• Critically evaluate the reasonableness of your answers.
• Manage your time effectively during exams.

Lesson summary

This week focuses on integrated exam preparation for Mathematical Literacy, using mixed, real-life tasks. This is crucial for Grade 12 learners as it simulates the type of questions found in the final examinations, which assess your ability to apply mathematical concepts to practical, everyday scenarios. By working through various types of problems, you will become more confident in identifying the relevant information, selecting the appropriate mathematical tools, and interpreting the results within the given context.

Lesson notes

This week integrates several core concepts from across the Mathematical Literacy curriculum.

Key areas to revise include: Measurement: Understanding units (metric and imperial), conversions, calculating area, volume, perimeter, and working with scale drawings.

Financial Mathematics: Simple and compound interest, budgets, income statements, calculating profit/loss, understanding taxes, loans, mortgages, and insurance.

Data Handling: Interpreting data from tables, charts, and graphs (bar graphs, pie charts, line graphs, scatter plots), calculating measures of central tendency (mean, median, mode), understanding range and interpreting data trends.

Probability: Basic probability calculations, understanding likelihood, and applying probability to real-life situations (e.g., lottery, insurance). Maps, Plans and other Representations of Physical Space: Interpreting scale, using bearings, calculating distances from maps and plans. Rates, Ratios and Proportions: Calculating rates of pay, currency exchange rates, direct and indirect proportion.

Number formats and conventions: Working with decimal numbers, rounding and estimation, significant figures.

Example 1: Housing Loan Calculation Thabo wants to buy a house in Soweto costing R850,

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0. He secures a loan for the full amount at an interest rate of 9.5% per annum, compounded monthly, repayable over 20 years. a) Calculate the monthly repayment. b) Calculate the total amount Thabo will repay over 20 years. c) Calculate the total interest Thabo will pay over the loan period.

Solution: a)

We use the loan repayment formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1] Where: M = Monthly payment P = Principal loan amount (R850,000) i = Monthly interest rate (9.5% per annum / 12 = 0.095/12 = 0.007916667) n = Number of months (20 years * 12 months/year = 240) M = 850000 [ 0.007916667(1 + 0.007916667)^240 ] / [ (1 + 0.007916667)^240 – 1] M = 850000 [ 0.007916667(5.9816...) ] / [ 5.9816... – 1] M = 850000 [ 0.04735... ] / [ 4.9816... ] M = 850000 * 0.009505075... M = R8079.31 (rounded to two decimal places) Therefore, Thabo's monthly repayment is R8079.31. b) Total repayment = Monthly payment * Number of months Total repayment = R8079.31 * 240 = R1,939,034.40 Therefore, Thabo will repay R1,939,034.40 over 20 years. c) Total interest = Total repayment - Principal loan amount Total interest = R1,939,034.40 - R850,000 = R1,089,034.40 Therefore, Thabo will pay R1,089,034.40 in interest over the loan period.

Example 2: Data Interpretation and Budgeting A local spaza shop owner, Maria, has the following monthly income and expenses: | Item | Amount (R) | |--------------|------------| | Sales Income | 15,000 | | Rent | 2,500 | | Stock | 8,000 | | Salaries | 3,000 | | Utilities | 1,000 | | Transport | 500 | a) Calculate Maria's total monthly expenses. b) Calculate Maria's monthly profit. c) Maria wants to increase her profit by 15%. How much more profit does she need to make? d) If Maria can reduce her stock expenses by 5%, calculate her new profit.

Solution: a) Total expenses = Rent + Stock + Salaries + Utilities + Transport Total expenses = R2,500 + R8,000 + R3,000 + R1,000 + R500 = R15,000 b) Monthly profit = Sales Income - Total expenses Monthly profit = R15,000 - R15,000 = R0 c) Increase in profit = Monthly profit 15% = R0 0.15 = R0 Maria's current profit is R0, so increasing this by 15% still yields a profit of R

0. To achieve a profit increase, she needs to address either increasing revenue or decreasing expenses. d) Reduction in stock expenses = R8,000 5% = R8,000 0.05 = R400 New stock expenses = R8,000 - R400 = R7,600 New total expenses = R2,500 + R7,600 + R3,000 + R1,000 + R500 = R14,600 New monthly profit = R15,000 - R14,600 = R400 Therefore, Maria's new profit is R

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0. Example 3: Map Scales and Distance Calculation A map of Gauteng has a scale of 1:500,

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0. The distance between Johannesburg and Pretoria on the map is 10 cm. a) Calculate the actual distance between Johannesburg and Pretoria in kilometers. b) If a taxi charges R12.50 per kilometer, calculate the cost of a taxi trip from Johannesburg to Pretoria.

Solution: a)

Map scale 1:500,000 means 1 cm on the map represents 500,000 cm in reality. Actual distance in cm = Map distance * Scale Actual distance in cm = 10 cm * 500,000 = 5,000,000 cm Convert cm to km: 5,000,000 cm / 100 cm/m / 1000 m/km = 50 km Therefore, the actual distance between Johannesburg and Pretoria is 50 km. b) Taxi cost = Distance * Rate per kilometer Taxi cost = 50 km * R12.50/km = R625.00 Therefore, the cost of a taxi trip from Johannesburg to Pretoria is R625.

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0. Guided Practice (With Solutions)

Question 1: Sipho wants to buy a new TV costing R6,

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0. He can either pay cash or buy it on hire purchase. The hire purchase agreement requires a 15% deposit and 24 monthly installments of R320. a) Calculate the deposit amount. b) Calculate the total amount Sipho will pay if he chooses the hire purchase option.